In imaging systems where the final output image has to be evaluated by a human observator a problem arises when the original image as obtained from an image sensing device contains detail information at various degrees of coarseness, within a wide amplitude range. This situation may arise when the sensor has a good signal to noise ratio over a large dynamic range, which is the case with computed radiography or computed tomography. When a typical image captured by such a device, e.g. a computed radiography image of a knee is to be represented on a film hardcopy (to be viewed on a lightbox) or even worse, on a display screen, then contrast of anatomic detail must always be traded of against dynamic range. Given the limited dynamic range of the image output medium (smaller than 500:1 in case of a transparent film, and smaller than 100:1 in case of a CRT screen under normal viewing conditions) then the tradeoff can be stated extremely as follows:
i) if the entire dynamic range of the diagnostically meaningful signal levels is mapped onto the available output medium dynamic range, then overall contrast will be very low, and for many subtle details, contrast will be below the perceptual threshold level, hence these will be missed by the observer. PA0 ii) if at the other hand only a part of the original dynamic range is mapped onto the output medium dynamic range then all signal levels below this range will all be mapped onto the same (low) output level, and all original levels exceeding this range will be mapped onto the same (high) output level. PA0 a) decomposing said original image into a sequence of detail images at multiple resolution levels and a residual image at a resolution level lower than the minimum of said multiple resolution levels, PA0 b) modifying the pixel values of said detail images to yield pixel values of a set of modified detail images according to at least one non-linear monotonically increasing odd conversion function with a slope that gradually decreases with increasing argument values, and PA0 c) computing said processed image by applying a reconstruction algorithm to the residual image and the modified detail images, the reconstruction algorithm being such that if it were applied to the residual image and the detail images without modification, then said original image or a close approximation thereof would be obtained. PA0 i) the mean of all pixel values in every detail image is zero; PA0 ii) the spatial frequency of every detail image is limited to a specific frequency band, said frequency band being defined as the compact region in the spatial frequency domain which contains nearly all (say 90%) of the spectral energy of the basic frequency period of said discrete detail image, adjusted to the original spatial frequency scale if said detail image contains less pixels than said original image; PA0 iii) every detail image corresponds to a different spatial frequency band, in such a way that the entire spatial frequency domain ranging from -pi to pi radians per pixel along both spatial frequency axes is covered by said spatial frequency bands associated with all said detail images considered within the decomposition; PA0 iv) each spatial frequency band associated with one of said detail images may partially overlap the neighboring bands without being fully included by a frequency band associated with another detail image; PA0 v) the number of pixels within each detail image is at least the number of pixels required by the Nyquist sampling criterion, so as to avoid aliasing, PA0 vi) at least two of said spatial frequency bands are considered in the course of said decomposition. PA0 a) decomposing said original image into a weighted sum of predetermined basic detail images at multiple resolution levels and a residual basic image by applying a transform to said image, said transform yielding a set of detail coefficients each expressing the relative contribution to the original image of one of a set of basis functions representing said basic detail images and a residual coefficient representing the relative contribution to the original image of a basis function representing said basic residual image, whereby said basis functions are continuous and non-periodic and have zero mean value except for the basis function that represents the basic residual image, and wherein said transform is characterised in that there exists an inverse transform which returns the original image or a close approximation thereof when being applied to said transform coefficients, PA0 b) modifying the detail coefficients according to at least one non-linear monotonically increasing odd mapping having a slope that gradually decreases with increasing absolute argument values, said function yielding a set of modified transform coefficients, PA0 c) computing said processed image by applying said inverse transform to the modified detail coefficients and the residual coefficient. PA0 i) the mean of all pixel values of every said basic detail image is zero; PA0 ii) every said subset covers the entire domain of said original image, i.e. for every pixel within said original domain there is within every said subset at least one basic detail image the spatial extent of which overlaps with said pixel; PA0 iii) all said basic detail images belonging to any particular subset are limited to the same spatial frequency band, said frequency band being defined as the compact region in spatial frequency domain which contains nearly all (say 90%) of the spectral energy of the basic frequency period of said basic detail image; PA0 iv) every said subset corresponds to a different spatial frequency band, in such a way that the entire spatial frequency band ranging from -pi through pi radians/pixel along both spatial frequency axes is covered by said spatial frequency bands associated with all said subsets considered within the decomposition; PA0 v) each spatial frequency band associated with one of said subsets may partially overlap the neighboring bands, without being fully included by a frequency band associated with another said subset; PA0 vi) at least two and preferably more said spatial frequency bands are considered in the course of said decomposition.
In that case only those image pixels having a level within the selected dynamic range will be presented with acceptable contrast, while the other pixels will have uniform brightness, and will show up with no contrast at all.
In image workstations connected to a computed radiography or computed tomography system the desired compromise between both extreme mappings is interactively selectable, a feature which is commonly referred to as window/level setting.
However in common working environments such as a hospital there is no time for selecting the optimal window/level compromise, so the question is very urgent to display a single image on film or monitor screen, which reveals all the relevant diagnostic details with an acceptable contrast over the whole dynamic range.
This problem is largely recognized in the field of digital radiology, see: Maack I., Neitzel U., "Optimized Image Processing for Routine Digital Radiography", Proceedings International Symposium CAR '91, p. 109, Springer Verlag.
A similar problem exists in the area of photofinishing and prepress, where images obtained from wide latitude films or scanning systems have to be printed on paper with good contrast across the whole density range, despite of the much smaller latitude of the reproduction medium.
Many attempts have been made to achieve this goal, such as the commonly known technique of unsharp masking, adaptive histogram equalisation, and the many variants on these generic methods, but all suffer to some extent from the shortcoming that ghost details, called artifacts are created in the vicinity of significant signal level transitions, which occur e.g. at bone/soft tissue boundaries within the image. These artifacts cause a serious problem since they might suggest pathological evidence in a normal radiograph, or in other cases such artifacts might hide subtle lesions. The detrimental effect of these artifacts on diagnosis are well described in literature: Rehm K., Dallas W. J., "Artifact Suppression in Digital Chest Radiographs Enhanced With Adaptive Histogram Equalization", Proceedings of SPIE, vol. 1092 Medical Imaging III, pp. 294-296, 1989, International Society for Optical Engineering, Bellingham; Oestmann J. W., Prokop M., Schaefer C. M., Galanski M., "Artefacts in Digital Storage Phospor Radiography", Proceedings International Symposium CAR '91, pp. 125, Springer Verlag; Bick U., Wiesmann W., Lenzen H., Fiebich M., von Lengerke H.-J., Peters P. E., "Utilizing digital luminescence radiography in pediatric radiology: a report of initial experiences", Electromedica, vol. 59, no.1, p.30, 1991.
Another problem with these contrast enhancement methods, which are based on the use of a sliding local operator, relates to the choice of the operator size. If one chooses a small operator size, only a few pixels diameter, then only the smaller details will be enhanced. With a larger operator size, larger details will be enhanced, at the expense of suppressing details of a different scale, which might be important as well. Adapting the operator size to the specific radiologic examination case may sometimes be feasible, but in many cases diagnostic details occur at different scale levels within the same image (even within close vicinity), in which case the results remain unsatisfactory despite fine tuning attempts. The multiple experimental studies on optimal parameter tuning for unsharp masking confirm that this is a non-trivial problem: Prokop M., Schaefer C., Oestmann J. W., Meschede A., Reichelt S., Galanski M., "Optimal Parameters for Unsharp Mask Filtering in Digital Chest Radiographs", Proceedings International Symposium CAR '91, pp. 149-154, Springer Verlag; Prokop M., Galanski M., Oestmann J. W., von Falkenhausen U., Rosenthal H., Reimer P., Nischelsky J., Reichelt S., "Storage Phosphor versus Screen-Film Radiography: Effect of Varying Exposure Parameters and Unsharp Mask Filtering on the Detectability of Cortical Bone Defects", Radiology vol. 177, no. 1, pp. 109-113, Oct. 1990.
In the field of digital image processing a novel paradigm of multiresolution computation has evolved the last decade, sometimes called pyramidal image processing. According to this concept multiple sets of processing parameters are used, tuned to a wide range of detail sizes. The basic concepts and efficient implementations of pyramidal decomposition are described in: Burr P. J., "Fast Filter Transforms for Image Processing", Computer Graphics and Image Processing, vol. 16, pp. 20-51, 1981; Crowley J. L., Stern R. M., "Fast Computation of the Difference of Low-Pass Transform", IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 6, no. 2, March 1984.
Alternative multiresolution representations are presented in: Mallat S. G., "A Theory for Multi resolution Signal Decomposition: The Wavelet Representation", IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 11, no. 7, July 1989; Ebrahimi T., Kunt M., "Image compression by Gabor Expansion", Optical Engineering, vol. 30, no. 7, pp. 873-880, July 1991.
Until now the main purpose of this kind of image processing techniques has been directed towards image compression: Arbeiter J. H., "Multi-dimensional video image processing architecture", Optical Engineering, vol. 25, no. 7, pp. 875-880, July 1986; Adelson E. H., Simoncelli E., and Hingorani R., "Orthogonal pyramid transforms for image coding", Proceedings of SPIE, vol. 845, pp. 50-58, 1987, International Society for Optical Engineering, Bellingham.
Other applications include multiresolution image segmentation, image interpolation, and filter synthesis with specified frequency response: Lifshitz L. M., Pizer S. N., "A Multiresolution Hierarchical Approach to Image Segmentation Based on Intensity Extrema", IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 12, no. 6, pp. 529-540, June 1990; Szeliski R., "Fast Surface Interpolation Using Hierarchical Basis Functions", IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 12, no. 6, pp. 513-528. June 1990; Ranganath S., "Image Filtering Using Multiresolution Representations", IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 13, no. 5, pp. 426-440, May 1991.